The midfielder is one of 16 players whose current deals run out at the end of the season and are free to speak to other clubs in January.
Increased competition for places has meant that Stevenson has featured in only five SPL games for the Easter Road side so far this season but the 22-year-old is enjoying life under Colin Calderwood's regime and is keen to force his way into the new manager's plans.
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Hide AdStevenson said: "Maybe in the last couple of seasons there were players who were more or less guaranteed a place in the side but that just doesn't happen now because there is so much competition.
"There are a lot of boys who have been involved and the manager has shown that he is not scared to change things around to see if something else works better.
"I think that everyone is up for the challenge. Obviously, there are a lot of contracts up at the end of the season and everyone is fighting for their future here really."
Stevenson was handed a start in Calderwood's first three matches, then dropped out of the side for the game against Rangers at Ibrox. He was back in as a second-half substitute for the home clash with Motherwell and is hoping to be involved this weekend when Hibs are due to take on St Johnstone at Easter Road.
"I am happy and enjoying the way that the new manager is doing things. I just have to keep working hard in training and take my chance if it comes along."